Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very high-resolution type of scanning probe microscopy, with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the optical diffraction limit. Accordingly over the past 30 years the AFM has become one of the foremost tools for imaging, measuring, and manipulating matter at the nanoscale level. The information is gathered by “feeling” the surface with a mechanical probe wherein piezoelectric elements facilitate tiny but precise movements under computer control. In some AFM variations electric potentials can also be scanned using conducting cantilevers whilst in others electrical currents are passed through the AFM tip to probe the electrical conductivity of the sample being characterized or manipulate atoms upon the underlying surface.
A frequency modulation atomic force microscope (FM-AFM) exploits a microscopic cantilever, with a sharp tip, which is oscillated above the surface of the sample being characterised. The interaction between this cantilever with the sample surface causes the resonance frequency of the cantilever to shift, which is detected via an FM demodulator and allegedly track the surface structure of the sample. The detected resonant frequency shift is then used via feedback loop to keep the cantilever oscillating at its resonant frequency and at constant amplitude. This technique facilitates the use of high Q cantilevers without restricting the bandwidth or the dynamic range of the technique. FM-AFM is typically used in ultra-high vacuum but has been reported within liquids as well. The FM-AFM method allows the measurement of forces with picoNewton (pN) resolution, as well as imaging and manipulating matter with sub-nanometer resolution.
Within the prior art energy dissipation measurements have been identified as both a complementary tool in FM-AFM and as providing additional information with respect to the FM-AFM technique for dynamic force measurement, see for example H. Hölscher et al in “Measurement of Conservative and Dissipative Tip-Sample Interaction Forces with a Dynamic Force Microscope using the Frequency Modulation Technique” (Phys. Rev. B, Vol. 64, No. 7, 075402, 6 pages) and P. M. Hoffmann et al in “Energy Dissipation in Atomic Force Microscopy and Atomic Loss Processes” (Phys. Rev. Lett. 87, 265502, 4 pages). However, to date the technique has generally not fulfilled expectations. Numerous theories have been developed for the interpretation of FM-AFM data, including S. Morita et al in “Non-Contact Atomic Force Microscopy—Volume 1” (Springer-Verlag), Hölscher and Hoffmann.
However, to date the unexplained variability in experimental data has prevented progress in AFM based energy dissipation studies and associated scientific insights and has led to many questions and controversies. The inventors have established that a significant source of the variability is the parasitic hardware resonances within the AFM which have been previously overlooked in the interpretation of dissipation data. The inventors have demonstrated that these unwanted resonances can change not only the quantitative but also the qualitative interpretation of dissipation data. Accordingly the inventors have been able to reconcile the discrepancies between predictions and experimental results. The inventors detailed analysis of FM-AFM demonstrates that drawing robust conclusions from dissipation experiments requires an accurate measurement of the transfer function of the piezoacoustic excitation system  used to oscillate the cantilever. Omitting this measurement can lead to false interpretation of changes in the drive signal which relate to the physics of the FM-AFM system being considered to be those arising from the tip-sample physics.
Previously the inventors, in “Decoupling Conservative and Dissipative Forces in Frequency Modulation Atomic Force Microscopy” (Phys. Rev. B, Vol. 84. 125433, 2011), discussed the different types of AFM studies that have thus far potentially been misinterpreted. Experiments and theoretical calculations of conservative forces measured by frequency modulation atomic force microscopy (FM-AFM) in vacuum within the prior art are generally in reasonable agreement. However, this contrasts with dissipative forces, where experiment and theory within the prior art often disagree by several orders of magnitude. The inventors demonstrated that the frequency response of the piezoacoustic cantilever excitation system, traditionally assumed flat, can actually lead to surprisingly large apparent damping by the coupling of the frequency shift to the drive-amplitude signal, typically referred to as the “dissipation” signal. Accordingly the large quantitative and qualitative variability observed in dissipation spectroscopy experiments, contrast inversion at step edges and in atomic-scale dissipation imaging, as well as changes in the power-law relationship between the drive signal and bias voltage in dissipation spectroscopy can be predicted. The magnitude of apparent damping can escalate by more than an order of magnitude at cryogenic temperatures.
Accordingly it would be beneficial for there to be a means of correcting this source of apparent damping allowing dissipation measurements to be reliably and quantitatively compared to theoretical models. It would be further beneficial for this method to be non-destructive and both easily and routinely integrated into FM-AFM measurements. According to embodiments of the invention a methodology is presented that can be directly implemented into standard AFM experimental protocols.
Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures.